Write the Word or Phrase That Best Completes Each Statement $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$

question 13

Essay

Write the word or phrase that best completes each statement or answers the question.
-Wildlife management personnel use predator-prey equations to model the populations of certain predators and
their prey in the wild. Suppose the population M of a predator after t months is given by $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$ while the population N of its primary prey is given by $$N = 12,250 + 3050 \cos \frac { \pi } { 6 } t$$ Find the values of $t , 0 \leq t < 12$ , for which the predator population is 875 . Find the values of $t , 0 \leq t < 12$ , for which the prey population is 10,725 .

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Definitions:

Direct Costs

Direct costs are expenses directly tied to the production of a product or service, such as raw materials and labor.

Marginal Tax Rate

The rate of tax applied to the next dollar of taxable income, indicating the percentage of additional income that is taken in taxes.

Amortizing

The process of paying off debt with a fixed repayment schedule in regular installments over a period of time, including both interest and principal.

Flotation Costs

Expenses incurred by a company in issuing new securities, including fees for underwriters, legal, accounting, and other registration and compliance costs.